. Differential and integral calculus. these singular points. 150. Multiple Points are those points of a curve common to twoor more of its branches. As the branches must either pass through the point or simplymeet at the point, there are two classes:1. The branches pass through the point. (i) (2) Fig. 34- (a) If the branches intersect, the point is called a Point of In-tersection; and the point is a double, triple, or quadruple . . point 208 Differential Calculus according as two, three, or four . . branches pass through i and 2 illustrate a double and a triple point. Since thecurve
. Differential and integral calculus. these singular points. 150. Multiple Points are those points of a curve common to twoor more of its branches. As the branches must either pass through the point or simplymeet at the point, there are two classes:1. The branches pass through the point. (i) (2) Fig. 34- (a) If the branches intersect, the point is called a Point of In-tersection; and the point is a double, triple, or quadruple . . point 208 Differential Calculus according as two, three, or four . . branches pass through i and 2 illustrate a double and a triple point. Since thecurve has as many tangents at a point of intersection as there are branches, it is obvious that — must have two different val-ues at a double point; three different values at a triple point;and so on. (b) If the branches touch as they pass through the point, it iscalled a Point of Osculation; and this point is of the first speciesor second species, according as the branches lie on opposite or onthe same side of their common (4) Fig. 34- Thus, Figs. (3) and (4) are illustrations of osculating points dyof the first and second species. Here — has two equal values. 2. The branches meet at the point. (a) If the branches have a common tangent at the point, thepoint is a Cusp of the first or second species, according as thebranches lie on opposite or on the same side of the tangent.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectcalculu, bookyear1918
